How to Align/Straighten/make Coplanar Non-planar edge between adjacent edges?
Apart rebuilding faces, as I said in comments above, here you find a possible way or sort of inspiration for a more "elegant" method, involving the "magic" Knife tool:

here is a similar setup to your situation:



we're going to use the knife tool to add a "guide" vertex to which we'll snap later, making the two selected faces planar again.



after activating the knife tool, it will show a green square when it "snaps" to a starting vertex: click here.



then, drag until it snaps the end vertex: click here too, then "confirm" pressing enter



note: the knife tool will "cut through" your mesh and create an intermediate vertex just where you need it (you see a preview before "confirming")



now you simply need to activate snap on vertixes, and drag your shared edge (locking Z in this case) until it snaps perfectly to the vertex just created by the knife tool





and now you just need to use "remove doubles" to remove the "guide vertex" we added before, and you're done!





Hth.